A hybrid estimator for generalized Pareto and extreme-value distributions

The methods of moments and probability-weighted moments are the most commonly used methods for estimating the parameters of the generalized Pareto distribution and generalized extreme-value distributions. These methods, however, frequently lead to nonfeasible estimates in the sense that the supports inferred from the estimates fail to contain all observations. In this paper, we propose a hybrid estimator which is derived by incorporating a simple auxiliary constraint; on feasibility into the estimates. The hybrid estimator is very easy to use, always feasible, and also has smaller bias and mean square error in many cases. Its advantages are further illustrated through the analyses of two real data sets.